GAME THEORY

Game theory is a branch of mathematical analysis
developed to study decision making in conflict situations. Such
a situation exists when two or more decision makers who have
different objectives act on the same system or share the same
resources. There are two person and multiperson games. Game
theory provides a mathematical process for selecting an OPTIMUM
STRATEGY (that is, an optimum decision or a sequence of
decisions) in the face of an opponent who has a strategy of his
own.

In game theory one usually makes the following assumptions:

(1) Each decision maker ["PLAYER"] has available to him two or
more well-specified choices or sequences of choices (called
"PLAYS").

(2) Every possible combination of plays available to the players
leads to a well-defined end-state (win, loss, or draw) that
terminates the game.

(3) A specified payoff for each player is associated with each
end-state (a [ZERO-SUM game] means that the sum of payoffs to
all players is zero in each end-state).

(4) Each decision maker has perfect knowledge of the game and of
his opposition; that is, he knows in full detail the rules of the
game as well as the payoffs of all other players.

(5) All decision makers are rational; that is, each player,
given two alternatives, will select the one that yields him the
greater payoff.

The last two assumptions, in particular, restrict the
application of game theory in real-world conflict situations.
Nonetheless, game theory has provided a means for analyzing many
problems of interest in economics, management science, and other
fields. (IIASA)

A general theory of rational behavior for situations in which (1) two (two-person games) or more (multi-person games) decision makers (players) have available to them (2) a finite number of courses of action (plays) each leading to (3) a well defined outcome or end with gains and losses expressed in terms of numerical payoffs associated with each combination of courses of action and for each decision maker. The decision makers have (4) perfect knowledge of the rules of the game, i.e., (1), (2) and (3) but no knowledge about the opponents' moves and are (5) rational in the sense of making decisions that optimize their individual gains. The matrix of payoffs can represent various conflicts. In a zero-sum game one person wins what the other loses. In other situations gains and losses may be unequally distributed which allows the representation of numerous competitive and conflict situations. The theory proposes several solutions, e.g., in a minimax strategy each participants minimizes the maximum loss the other can impose on him, a mixed strategy involves probabilistic choices. Experiments with such games revealed conditions for cooperation, defection and the persistence of conflict. The theory and some of the results have found applications in economics, management science bargaining and conflict resolution among many areas of interest. (Krippendorff)